Bulletin of the Korean Mathematical Society (대한수학회보)

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M-INJECTIVITY AND ASYMPTOTIC BEHAVIOUR

  • Toroghy, H.-Ansari (Department of Mathematics, Faculty of Science, Guilan University)
  • Published : 2002.05.01
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Abstract

Let R be a commutative Noetherian ring and M an R-module. In this paper we will consider the asymptotic behaviour of ideals relative to an R-module E which is M-injective.

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References

  1. Frank W. Anderson and Kent R. Fuller, Categories of Modules (second edition), Springer-Verlag New York, 1992.
  2. H. Ansari-Toroghy and R. Y. Sharp, Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings, Proc. Edinb. Math. Soc. 34 (1991), no. 2, 155-160. https://doi.org/10.1017/S0013091500005071
  3. N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading Mass., 1972.
  4. N. Brodmann, Asymptotic stability of Ass( M/$I^{n}$M), Proc. Amer. Math. Soc. 74 (1979), 16-18 https://doi.org/10.1090/S0002-9939-1979-0521865-8
  5. I. G. Macdonald, Secondary representation of modules over a commutative ring, Symp. Math. XI (1973), 23-43.
  6. E. Matlis, Injective modules over Noetherian rings, Pacific J. Math. 8 (1958), 511-528. https://doi.org/10.2140/pjm.1958.8.511
  7. L. Melkerson and P. Schenzel, Asymptotic attached prime ideals related to injective modules, Comm. Algebra 20 (1992), no. 2, 583-590. https://doi.org/10.1080/00927879208824358
  8. R. Y. Sharp, A method for study of Artinian modules, with an application to asymptotic behaviour, In "Commutative Algebra, Math Sience Research lnst. Publ. No. 15." Springer- Verlag, New York, 1989, pp. 443-465.
  9. S. Yassemi, Coassociated primes, Comm. Algebra 23 (1995), 1473-1498. https://doi.org/10.1080/00927879508825288
  10. S. Yassemi, Coassociated primes of modules over a commutative ring, Math. Scand. 80 (1997), 175-187. https://doi.org/10.7146/math.scand.a-12617